Triple

T20471196
Position Surface form Disambiguated ID Type / Status
Subject Hermite–Minkowski theorem E502195 entity
Predicate relatedTo P37 FINISHED
Object Hermite’s constant NE NERFINISHED

How this triple was built (2 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Hermite’s constant | Statement: [Hermite–Minkowski theorem, relatedTo, Hermite’s constant]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Hermite’s constant
Context triple: [Hermite–Minkowski theorem, relatedTo, Hermite’s constant]
  • A. Hermite constant chosen
    The Hermite constant is a number in each dimension that measures the densest possible lattice sphere packing, playing a central role in the geometry of numbers and lattice theory.
  • B. Hermite–Minkowski theorem
    The Hermite–Minkowski theorem is a fundamental result in algebraic number theory that gives a finiteness bound on the number of number fields of a given degree and discriminant.
  • C. Koksma–Hlawka inequality
    The Koksma–Hlawka inequality is a fundamental result in numerical analysis and discrepancy theory that bounds the error of quasi-Monte Carlo integration by the product of a function’s variation and the discrepancy of the sampling points.
  • D. Liouville's inequality in Diophantine approximation
    Liouville's inequality in Diophantine approximation is a foundational result that gives explicit lower bounds on how closely algebraic numbers can be approximated by rationals, leading to the first examples of transcendental numbers.
  • E. Hurwitz determinants
    Hurwitz determinants are specific determinants constructed from a polynomial’s coefficients that are used to test whether all roots of the polynomial lie in the left half of the complex plane, thereby assessing system stability.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (2 batches)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step Stage Batch ID Status When
creating Elicitation batch_69e0b4ae5f1081908768b0c9a3a0bf38 completed April 16, 2026, 10:06 a.m.
NER Named-entity recognition batch_69e699608d7c8190910217817e789915 completed April 20, 2026, 9:23 p.m.
Created at: April 16, 2026, 11:33 a.m.